Quasicrystals are materials with atoms arranged in a non-periodic but ordered pattern. To describe their electronic properties, we consider hybridization of their valence electrons similar to what is done for periodic materials, e.g., by constructing a Kronig–Penney model for nearly-free electrons in the corresponding quasiperiodic potential energy landscape [1]}, see Fig. REF  for an illustration of a quasiperiodic 1D chain. As we discuss below, such a construction lends itself also to metamaterial structures, where waves interfere in the presence of a patterned medium. Assuming sufficiently-spaced and sufficiently-deep potential wells allows labeling of the resulting spectral band structures according to the separated orbits of the individual potential wells, e.g., by s-, p-, and d-like orbital bands. On top of this orbital separation, the longer-ranged quasiperiodic spatial arrangement of the “atoms” leads to splitting of the bands into infinitely-many mini-bands.
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